Aeroacoustics of Low Mach Number Flows : Fundamentals, Analysis, and Measurement

Aeroacoustics of Low Mach Number Flows: Fundamentals, Analysis, and Measurement provides a comprehensive treatment of sound radiation from subsonic flow over moving surfaces, which is the most widespread cause of flow noise in engineering systems. This includes fan noise, rotor noise, wind turbine noise, boundary layer noise, and aircraft noise. Beginning with fluid dynamics, the fundamental equations of aeroacoustics are derived and the key methods of solution are explained, focusing both on the necessary mathematics and physics. Fundamentals of turbulence and turbulent flows, experimental methods and numerous applications are also covered. The book is an ideal source of information on aeroacoustics for researchers and graduate students in engineering, physics, or applied math, as well as for engineers working in this field. Supplementary material for this book is provided by the authors on the website www.aeroacoustics.net. The website provides educational content designed to help students and researchers in understanding some of the principles and applications of aeroacoustics, and includes example problems, data, sample codes, course plans and errata. The website is continuously being reviewed and added to. Explains the key theoretical tools of aeroacoustics, from Lighthill’s analogy to the Ffowcs Williams and Hawkings equation Provides detailed coverage of sound from lifting surfaces, boundary layers, rotating blades, ducted fans and more Presents the fundamentals of sound measurement and aeroacoustic wind tunnel testing Part 1: Fundamentals 1: Introduction Abstract 1.1 Aeroacoustics of low Mach number flows 1.2 Sound waves and turbulence 1.3 Quantifying sound levels and annoyance 1.4 Symbol and analysis conventions used in this book 2: The equations of fluid motion Abstract 2.1 Tensor notation 2.2 The equation of continuity 2.3 The momentum equation 2.4 Thermodynamic quantities 2.5 The role of vorticity 2.6 Energy and acoustic intensity 2.7 Some relevant fluid dynamic concepts and methods 3: Linear acoustics Abstract 3.1 The acoustic wave equation 3.2 Plane waves and spherical waves 3.3 Harmonic time dependence 3.4 Sound generation by a small sphere 3.5 Sound scattering by a small sphere 3.6 Superposition and far field approximations 3.7 Monopole, dipole, and quadrupole sources 3.8 Acoustic intensity and sound power output 3.9 Solution to the wave equation using Green's functions 3.10 Frequency domain solutions and Fourier transforms 4: Lighthill's acoustic analogy Abstract 4.1 Lighthill's analogy 4.2 Limitations of the acoustic analogy 4.3 Curle's theorem 4.4 Monopole, dipole, and quadrupole sources 4.5 Tailored Green's functions 4.6 Integral formulas for tailored Green's functions 4.7 Wavenumber and Fourier transforms 5: The Ffowcs Williams and Hawkings equation Abstract 5.1 Generalized derivatives 5.2 The Ffowcs Williams and Hawkings equation 5.3 Moving sources 5.4 Sources in a free stream 5.5 Ffowcs Williams and Hawkings surfaces 5.6 Incompressible flow estimates of acoustic source terms 6: The linearized Euler equations Abstract 6.1 Goldstein's equation 6.2 Drift coordinates 6.3 Rapid distortion theory 6.4 Acoustically compact thin airfoils and the Kutta condition 6.5 The Prantl–Glauert transformation 7: Vortex sound Abstract 7.1 Theory of vortex sound 7.2 Sound from two line vortices in free space 7.3 Surface forces in incompressible flow 7.4 Aeolian tones 7.5 Blade vortex interactions in incompressible flow 7.6 The effect of angle of attack and blade thickness on unsteady loads 8: Turbulence and stochastic processes Abstract 8.1 The nature of turbulence 8.2 Averaging and the expected value 8.3 Averaging of the governing equations and computational approaches 8.4 Descriptions of turbulence for aeroacoustic analysis 9: Turbulent flows Abstract 9.1 Homogeneous isotropic turbulence 9.2 Inhomogeneous turbulent flows Part 2: Experimental approaches 10: Aeroacoustic testing and instrumentation Abstract 10.1 Aeroacoustic wind tunnels 10.2 Wind tunnel acoustic corrections 10.3 Sound measurement 10.4 The measurement of turbulent pressure fluctuations 10.5 Velocity measurement 11: Measurement, signal processing, and uncertainty Abstract 11.1 Limitations of measured data 11.2 Uncertainty 11.3 Averaging and convergence 11.4 Numerically estimating fourier transforms 11.5 Measurement as seen from the frequency domain 11.6 Calculating time spectra and correlations 11.7 Wavenumber spectra and spatial correlations 12: Phased arrays Abstract 12.1 Basic delay and sum processing 12.2 General approach to array processing 12.3 Deconvolution methods 12.4 Correlated sources and directionality Part 3: Edge and boundary layer noise 13: The theory of edge scattering Abstract 13.1 The importance of edge scattering 13.2 The Schwartzschild problem and its solution based on the Weiner Hopf method 13.3 The effect of uniform flow 13.4 The leading edge scattering problem 14: Leading edge noise Abstract 14.1 The compressible flow blade response function 14.2 The acoustic far field 14.3 An airfoil in a turbulent stream 14.4 Blade vortex interactions in compressible flow 15: Trailing edge and roughness noise Abstract 15.1 The origin and scaling of trailing edge noise 15.2 Amiet's trailing edge noise theory 15.3 The method of Brooks, Pope, and Marcolini [8] 15.4 Roughness noise Part 4: Rotating blades and duct acoustics 16: Open rotor noise Abstract 16.1 Tone and broadband noise 16.2 Time domain prediction methods for tone noise 16.3 Frequency domain prediction methods for tone noise 16.4 Broadband noise from open rotors 16.5 Haystacking of broadband noise 16.6 Blade vortex interactions 17: Duct acoustics Abstract 17.1 Introduction 17.2 The sound in a cylindrical duct 17.3 Duct liners 17.4 The Green's function for a source in a cylindrical duct 17.5 Sound power in ducts 17.6 Nonuniform mean flow 17.7 The radiation from duct inlets and exits 18: Fan noise Abstract 18.1 Sources of sound in ducted fans 18.2 Duct mode amplitudes 18.3 The cascade blade response function 18.4 The rectilinear model of a rotor or stator in a cylindrical duct 18.5 Wake evolution in swirling flows 18.6 Fan tone noise 18.7 Broadband fan noise Appendix A: Nomenclature A.1 Symbol conventions, symbol modifiers, and Fourier transforms A.2 Symbols used Appendix B: Branch cuts Appendix C: The cascade blade response function Index Focusing both on the necessary mathematics and physics, this resource provides a comprehensive treatment of sound radiation from subsonic flow over moving surfaces, which is the most widespread cause of flow noise in engineering systems. -- Edited summary from book